Tottenham Hotspur are also said to be interested in the Danish international.
The central defender, one of the stars of the summer's European Under-21 Championships, was linked with the Premier League sides in the summer.
The Dane however made it clear that he had no intention of leaving the Bundesliga side and instead stayed at Werder Bremen.
The reports today however suggest Newcastle and Everton are back in for the player - along with Tottenham - as Werder Bremen seek to sell after horrific financial results.
Fussball Transfers report, quoting the print version of Bild, that Werder Bremen have posted a €6 million loss this year on the back of an already troubled financial situation.
Therefore both Vestergaard and striker Anthony Ujah are believed to be available for transfer in January - with the Premier League trio said to be considering a move for the Danish defender.